1. Field of the Invention
The invention relates to an acceleration and deceleration method, particularly to an acceleration and deceleration method which is suitable for application of the hand of a robot and for an operating portion of a machine tool.
2. Description of Prior Art
The prior machine tool and robot are linearly accelerated and decelerated at the beginning and deceleration of axially transferring, so that the mechanism gets a shock, and has bad linearity and discontinuity of speed while transferring objects.
For example, FIG. 1 is a graph showing relation among speed of transferring objects, speed in the x direction, and in the y direction, and transferring distance.
In FIG. 1, (Xi,Yi) are the coordinates of current position for transferring objects, and (Xf,Yf) are the coordinates of the destination position. If V is the rectilinearly transferring speed of objects from current position to destination position, the x-component .DELTA.X and y-component .DELTA.Y of the transfer distance are EQU .DELTA.X=.vertline.XF-Xi.vertline. (1) EQU .DELTA.Y=.vertline.Yf-Yi.vertline. (2)
and transferring speed Vx,Vy in the x direction and y direction are : ##EQU1## For example, the coordinates of the current position are (Xi,Yi)=(100,100), and the coordinates of the destination position are (Xf,Yf)=(8100, 6100), and the rectilinearly transfer speed of object is V=180 pulse/msec, x-component .DELTA.X, y-component .DELTA.Y of the transfer distance are: EQU .DELTA.X=.vertline.Xf-Xi.vertline.=.vertline.8100-100.vertline.=8000 pulse EQU .DELTA.Y=.vertline.Yf-Yi.vertline.=.vertline.6100-100.vertline.=6000 pulse, and
X-component Vx, Y-component Vy of transfer speed are: ##EQU2## If the current position (Xi, Yi), the destination position (Xf, Yf) and rectilinearly transfer speed are given, we get x-direction distance X, and y-direction distance Y of transfer distance and x-direction speed Vx, y-direction speed Vy of the transfer speed.
When the transferring mechanism transfers an object with linear acceleration and deceleration while rectilinearly transferring the object such as shown in FIG. 2, area of AB'C'D and area of ABCD in FIG. 2 are the y-direction transferring distance .DELTA.Y and x-direction transfer distance .DELTA.X, and ##EQU3## must be constant in rectilinearly transference at k. If said ratio is constant, the object is rectilinearly transferred from current position to destination position. Accordingly, the ratio is calculated respectively in accelerating period, in decelerating period and in uniform speed period, so that transferring mechanism decides whether or not the ratio is constant, and also the transfer distance Sx in the x-direction and transfer distance Sy in the y-direction at every sampling time are obtained by calculating the following equations: ##STR1## As described in the process, much time is spent on calculation of the equation, so that sampling time becomes unsuitably long to detect current position of the transfer object, and the degree of linearity of the transferred object is bad. Also discontinuity of speed is generated in B,C and B',C' as shown in FIG. 2, thus rectilinear transference is distorted at the discontinued point of speed.
Also, in Japanese Patent Published NO.SHO 61-245209, in order not to generate shock and concussion to the transferring mechanism at the beginning and deceleration of axis transference, the apparatus described in that document uses a the first algorithm portion in which the transferring components are piled up one on another at each sampling time, the second algorithm portion which takes a weighted average of the transferring components and a stage which sets up repeat parameters of the first and second algorithm portion, to enable control of exponential acceleration and deceleration by outputting values resulting from the second algorithm portion as speed command. Because the apparatus achieves exponential acceleration and deceleration by hardware, and because the circuitry needed to compose that hardware requires a large number of electronic components, the manufacturing process for constructing the process needed to compose said hardware is complicated.